5 papers
Unbalanced Optimal Transport Dictionary Learning for Unsupervised Hyperspectral Image Clustering
Joshua Lentz, Nicholas Karris, Alex Cloninger +1
Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical…
Optimal Transport, Timesteppers, Newton-Krylov Methods and Steady States of Collective Particle Dynamics
Hannes Vandecasteele, Nicholas Karris, Alexander Cloninger +1
Timesteppers constitute a powerful tool in modern computational science and engineering. Although they are typically used to advance the system forward in time, they can also be vi…
Which Way from B to A: The role of embedding geometry in image interpolation for Stable Diffusion
Nicholas Karris, Luke Durell, Javier Flores +1
It can be shown that Stable Diffusion has a permutation-invariance property with respect to the rows of Contrastive Language-Image Pretraining (CLIP) embedding matrices. This inspi…
Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systems
Nicholas Karris, Evangelos A. Nikitopoulos, Ioannis G. Kevrekidis +2
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use lineariz…
Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds
Jun Linwu, Varun Khurana, Nicholas Karris +1
The pyLOT library offers a Python implementation of linearized optimal transport (LOT) techniques and methods to use in downstream tasks. The pipeline embeds probability distributi…